The invention relates to a sewing method and a sewing machine for sewing on a piece to be sewn such as a flexible cover, a stitch consisting of threads, known as auxiliary threads, of the type which form a passage which extends in the direction of sewing (oversewing, zig-zag, etc), with a thread, known as the tension thread, which is guided and put into position relative to the stitch in the passage, simultaneously with picking up of the auxiliary threads, such that this tension thread can slide longitudinally and/or laterally in this passage, the tension thread not being picked up by the auxiliary threads which form the stitch.